Geometric indices and the Alexander polynomial of a knot期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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Geometric indices and the Alexander polynomial of a knot

Authors:	Hirozumi Fujii

Institution:	Department of Mathematics, Osaka City University, Sugimoto, Sumiyoshi, Osaka, Japan

Abstract:	It is well-known that any Laurent polynomial $\Delta (t)$ satisfying $\Delta (t)\allowbreak \doteq \Delta (t^{-1})$ and $\Delta (1) = \pm 1$ is the Alexander polynomial of a knot in . We show that $\Delta (t)$ can be realized by a knot which has the following properties simultaneously: (i) tunnel number 1; (ii) bridge index 3; and (iii) unknotting number 1.

Keywords:	Tunnel number bridge index Alexander polynomial

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